Australian mathematician
Akshay Venkatesh
FRS
(born 21 November 1981) is an Australian
mathematician
and a professor (since 15 August 2018) at the School of Mathematics at the
Institute for Advanced Study
.
[1]
His research interests are in the fields of
counting
,
equidistribution
problems in
automorphic forms
and
number theory
, in particular
representation theory
,
locally symmetric spaces
,
ergodic theory
, and
algebraic topology
.
[2]
He was the first Australian to have won medals at both the
International Physics Olympiad
and
International Mathematical Olympiad
, which he did at the age of 12.
[3]
[4]
In 2018, he was awarded the
Fields Medal
for his synthesis of
analytic number theory
,
homogeneous dynamics
,
topology
, and
representation theory
.
[5]
[6]
He is the second Australian
[7]
and the second person of Indian descent to win the Fields Medal.
[8]
He was on the Mathematical Sciences jury for the
Infosys Prize
in 2020.
[9]
Early years
[
edit
]
Akshay Venkatesh was born in
Delhi
, India, in a Tamil Brahmin family and his family emigrated to
Perth
in
Western Australia
when he was two years old. He attended
Scotch College
. His mother,
Svetha
, is a
computer science
professor at
Deakin University
. A
child prodigy
, Akshay attended extracurricular training classes for gifted students in the state mathematical olympiad program,
[10]
and in 1993, whilst aged only 11, he competed at the 24th
International Physics Olympiad
in
Williamsburg, Virginia
, winning a bronze medal.
[11]
The following year, he switched his attention to mathematics and, after placing second in the
Australian Mathematical Olympiad
,
[12]
he won a silver medal in the 6th
Asian Pacific Mathematics Olympiad
,
[13]
before winning a bronze medal at the 1994
International Mathematical Olympiad
held in Hong Kong.
[3]
He completed his secondary education the same year, turning 13 before entering the
University of Western Australia
as its youngest ever student. Venkatesh completed the four-year course in three years and became, at 16, the youngest person to earn
First Class Honours
in
pure mathematics
from the university.
[3]
He was awarded the J. A. Woods Memorial Prize as the most outstanding graduate of the year from the Faculties of Science, Engineering, Dentistry, or Medical Science.
[14]
[15]
While at UWA he was also one of the founding members of the Honours Cricket Association.
[16]
Research career
[
edit
]
Akshay commenced his PhD at
Princeton University
in 1998 under
Peter Sarnak
, which he completed in 2002,
[2]
producing the thesis
Limiting forms of the trace formula
. He was supported by the Hackett Fellowship for postgraduate study. He was then awarded a postdoctoral position at the
Massachusetts Institute of Technology
, where he served as a
C.L.E. Moore instructor
. Venkatesh then held a Clay Research Fellowship from the
Clay Mathematics Institute
from 2004 to 2006,
[2]
and was an associate professor at the
Courant Institute of Mathematical Sciences
at
New York University
.
[17]
[18]
He was a member of the School of Mathematics at the
Institute for Advanced Study
(IAS) from 2005 to 2006. He became a
full professor
at
Stanford University
on 1 September 2008. After serving as distinguished visiting professor at the IAS in 2017?2018,
[17]
he became a permanent faculty member of IAS in August 2018.
[19]
Recognition
[
edit
]
Akshay was awarded the
Salem Prize
, given to a "young mathematician judged to have done outstanding work in
Salem's
field of interest—the theory of
Fourier series
"
[20]
and the
Packard Fellowship
in 2007. In 2008, he received the US$10,000
SASTRA Ramanujan Prize
, given for "outstanding contributions to areas of mathematics influenced by the great Indian mathematician,
Srinivasa Ramanujan
" and "only awarded to those under the age of thirty-two (the age of Ramanujan at his time of death)."
[3]
[21]
The prize was presented at the International Conference on Number Theory and Modular Forms, held at
SASTRA University
in
Kumbakonam
, Ramanujan's hometown.
[21]
In 2010, he was an
invited speaker at the International Congress of Mathematicians
(Hyderabad) and spoke on the topic "Number Theory and Lie Theory and Generalisations."
[22]
For his exceptionally wide-ranging, foundational and creative contributions to modern number theory, Venkatesh was awarded the
Infosys Prize
in Mathematical Sciences
[23]
in 2016. In 2017 he received the
Ostrowski Prize
,
[24]
which is awarded every two years for "outstanding achievements in pure mathematics and in the foundations of numerical mathematics."
[25]
In 2018, he was awarded the
Fields Medal
,
[5]
[26]
commonly described as the Nobel Prize of mathematics,
[27]
becoming the second Australian (after
Terence Tao
)
[7]
and the second person of Indian descent (after
Manjul Bhargava
)
[8]
to be so honoured. The short citation for the medal declared that Venkatesh was being honoured for "his synthesis of analytic number theory, homogeneous dynamics, topology, and representation theory, which has resolved long-standing problems in areas such as the equidistribution of arithmetic objects."
[6]
University of Western Australia
Professor Michael Giudici said of his former classmate's work that "[i]f it was easy for me to explain, then he wouldn't have received the Fields Medal".
[27]
Australian mathematician and media personality
Adam Spencer
said that "[t]his century will be built by mathematicians, whether it's computer coding, algorithms, machine learning, artificial intelligence, app design and the like" and that "we should acknowledge the magnificence of the mathematical mind."
[26]
Director of the
Australian Mathematical Sciences Institute
Professor Geoff Prince said "Akshay is an exciting and innovative leader in his field whose work will continue to have wide-ranging implications for mathematics" and a worthy recipient of the Fields medal "given his contribution to improving mathematicians' understanding of analytic number theory, algebraic number theory, and representation theory".
[28]
The long citation for his Fields Medal describes Venkatesh as having "made profound contributions to an exceptionally broad range of subjects in mathematics" and recognises that he "solved many longstanding problems by combining methods from seemingly unrelated areas, presented novel viewpoints on classical problems, and produced strikingly far-reaching conjectures."
[6]
[29]
Venkatesh's "use of dynamics theory, which studies the equations of moving objects to solve problems in number theory, which is the study of whole numbers, integers and prime numbers" was recognised in the award.
[7]
"His work uses representation theory, which represents abstract algebra in terms of more easily-understood linear algebra, and topology theory, which studies the properties of structures that are deformed through stretching or twisting, like a Mobius strip."
[7]
He described his work in 2016 as "looking for new patterns in the arithmetic of numbers".
[7]
On receiving the award, which is presented every four years, Venkatesh said "A lot of the time when you do math, you're stuck, but at the same time there are all these moments where you feel privileged that you get to work with it. You have this sensation of transcendence, you feel like you've been part of something really meaningful."
[7]
Contributions to mathematics
[
edit
]
Akshay has made contributions to a wide variety of areas in mathematics, including
number theory
,
automorphic forms
,
representation theory
,
locally symmetric spaces
and
ergodic theory
, by himself, and in collaboration with several mathematicians.
[6]
Using
ergodic
methods, Venkatesh, jointly with
Jordan Ellenberg
, made significant progress on the
Hasse principle
for integral representations of quadratic forms by quadratic forms.
[6]
[30]
In a series of joint works with
Manfred Einsiedler
,
Elon Lindenstrauss
and
Philippe Michel
, Venkatesh revisited the Linnik ergodic method and solved a longstanding conjecture of
Yuri Linnik
on the distribution of torus orbits attached to cubic number fields.
[6]
[31]
Akshay Venkatesh also provided a novel and more direct way of establishing sub-convexity estimates for
L-functions
in numerous cases, going beyond the foundational work of Hardy?Littlewood?Weyl, Burgess, and Duke?Friedlander?Iwaniec that dealt with important special cases.
[6]
[32]
[33]
This approach eventually resulted in the complete resolution by Venkatesh and
Philippe Michel
of the sub-convexity problem for GL(1) and GL(2) L-functions over general number fields.
[33]
References
[
edit
]
- ^
"Akshay Venkatesh"
.
Institute for Advanced Study
. Retrieved
7 August
2019
.
- ^
a
b
c
"Akshay Venkatesh"
.
claymath.org
.
Clay Mathematics Institute
. 2 August 2018
. Retrieved
4 August
2018
.
- ^
a
b
c
d
"Former IMO Olympians"
.
amt.edu.au
.
Australian Mathematics Trust
. 2017. Archived from
the original
on 13 December 2018
. Retrieved
4 August
2018
.
- ^
MacDonald, Janine (15 July 2011).
"Maths boy wonder shows how to stack oranges"
(Press release).
University of Western Australia
. Retrieved
4 August
2018
.
- ^
a
b
"Fields Medals 2018"
.
mathunion.org
.
International Mathematical Union
. 2018
. Retrieved
4 August
2018
.
- ^
a
b
c
d
e
f
g
"Venkatesh Short and Long Citation"
(PDF)
.
mathunion.org
.
International Mathematical Union
. 2018
. Retrieved
4 August
2018
.
- ^
a
b
c
d
e
f
Zhou, Naaman (2 August 2018).
"Australian Akshay Venkatesh wins Fields medal ? the 'Nobel for maths'
"
.
Guardian Australia
. Retrieved
4 August
2018
.
- ^
a
b
"Indian-origin mathematician Akshay Venkatesh maths 'Nobel' Fields Medal"
.
India TV News
. 2 August 2018
. Retrieved
4 August
2018
.
- ^
"Infosys Prize - Jury 2020"
.
www.infosys-science-foundation.com
. Retrieved
10 December
2020
.
- ^
Schultz, Phill (24 January 2005).
"My Automathography – 30 Years at UWA"
.
University of Western Australia
. Archived from
the original
on 24 March 2015
. Retrieved
4 August
2018
.
- ^
"XXIV International Physics Olympiad Williamsburg"
. 1993. Archived from
the original
on 5 February 2012
. Retrieved
7 June
2013
.
- ^
"Highest AMO scorers, 1994"
. Australian Mathematics Trust. Archived from
the original
on 24 March 2012
. Retrieved
7 June
2013
.
- ^
"Results of 6th Asian Pacific Mathematics Olympiad 1994"
. Australian Mathematics Trust. Archived from
the original
on 29 April 2013
. Retrieved
7 June
2013
.
- ^
"Conditions – J. A. Wood Memorial Prizes [F1495-03]"
.
University of Western Australia
. 3 November 2015
. Retrieved
4 August
2018
.
- ^
Stacey, David (2 August 2018).
"UWA maths prodigy wins international award"
(Press release).
University of Western Australia
. Retrieved
4 August
2018
.
- ^
"Honours Cricket Association"
. Honours Cricket Association. Archived from
the original
on 13 December 2002
. Retrieved
22 August
2019
.
- ^
a
b
"Akshay Venkatesh"
.
Institute for Advanced Study
. 2018
. Retrieved
4 August
2018
.
- ^
"Akshay Venkatesh – Research Interests"
.
math.stanford.edu
.
Stanford University
. Retrieved
4 August
2018
.
- ^
"Mathematician Akshay Venkatesh Appointed to the Faculty of the Institute for Advanced Study"
(Press release).
Institute for Advanced Study
. 2018
. Retrieved
6 August
2018
.
- ^
"NYU's Venkatesh, 25, Wins Prize Given to Young Mathematicians for Work in Field of Analysis"
(Press release).
New York University
. 22 August 2007
. Retrieved
4 August
2018
.
- ^
a
b
"Venkatesh Awarded 2008 SASTRA Ramanujan Prize"
(PDF)
.
Notices of the AMS
.
56
(1): 56. January 2009.
- ^
"ICM Plenary and Invited Speakers since 1897"
.
mathunion.org
.
International Mathematical Union
. 11 June 2016. Archived from
the original
on 11 June 2016
. Retrieved
16 May
2016
.
- ^
"Infosys Prize ? Laureates 2016 ? Prof. Akshay Venkatesh"
.
www.infosys-science-foundation.com
. Retrieved
3 April
2017
.
- ^
"Citation for Akshay Venkatesh"
(PDF)
.
ostrowski.ch
.
Ostrowski Foundation
. 2017
. Retrieved
4 August
2018
.
- ^
"Foundation A. M. Ostrowski for an international prize in higher mathematics"
.
Ostrowski.ch
.
Ostrowski Foundation
. 2018
. Retrieved
4 August
2018
.
- ^
a
b
Keane, Daniel (2 August 2018).
"Maths hands out its 'Nobel Prize' to an Australian ? here's why you should care"
.
ABC News
. Retrieved
2 August
2018
.
- ^
a
b
Slezak, Michael (2 August 2018).
"Fields Medal: Aussie genius Akshay Venkatesh wins 'Nobel Prize of mathematics'
"
.
ABC News
. Retrieved
4 August
2018
.
- ^
"Aussie Akshay Venkatesh wins 'the Nobel Prize of mathematics'
"
.
SBS News
. AAP. 2 August 2018
. Retrieved
4 August
2018
.
- ^
"Australian mathematician wins Fields Medal"
.
science.org.au
(Press release).
Australian Academy of Science
. 3 August 2018
. Retrieved
4 August
2018
.
- ^
Ellenberg, Jordan S.
; Venkatesh, Akshay (2008). "Local-global principles for representations of quadratic forms".
Inventiones Mathematicae
.
171
(2): 257?279.
arXiv
:
math/0604232
.
Bibcode
:
2007InMat.171..257E
.
CiteSeerX
10.1.1.236.7085
.
doi
:
10.1007/s00222-007-0077-7
.
S2CID
832133
.
- ^
Einsiedler, Manfred
;
Lindenstrauss, Elon
;
Michel, Philippe
; Akshay, Akshay (2011).
"Distribution of periodic torus orbits and Duke's theorem for cubic fields"
.
Annals of Mathematics
.
173
(2): 815?885.
arXiv
:
0708.1113
.
doi
:
10.4007/annals.2011.173.2.5
.
S2CID
6236918
.
- ^
Venkatesh, Akshay (2010).
"Sparse equidistribution problems, period bounds and subconvexity"
.
Annals of Mathematics
.
172
(2): 989?1094.
arXiv
:
math/0506224
.
doi
:
10.4007/annals.2010.172.989
.
S2CID
119163205
.
- ^
a
b
Michel, Philippe
; Venkatesh, Akshay (2010). "The subconvexity problem for GL
2
".
Publications Mathematiques de l'IHES
.
111
(1): 171?271.
arXiv
:
0903.3591
.
CiteSeerX
10.1.1.750.8950
.
doi
:
10.1007/s10240-010-0025-8
.
S2CID
14155294
.
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